Geodesic
The minimal $\Phi$-Lagrangian surfaces in almost Hermitian manyfolds
Sbornik. Mathematics, Tome 67 (1990) no. 2, pp. 379-391 Cet article a éte moissonné depuis la source Math-Net.Ru

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A general method of calibrations is developed for the study of minimal $\Phi$-Lagrangian surfaces in almost-Hermitian manifolds. A criterion for minimality of $\Phi$-Lagrangian surfaces is given, along with a lower bound for the second variation of the volume functional on minimal $\Phi$-Lagrangian surfaces in Hermitian manifolds. The generalized Maslov index of these surfaces is shown to be trivial. Bibliography: 11 titles. 
@article{SM_1990_67_2_a3,
     author = {L\^e H\^ong V\^an},
     title = {The minimal $\Phi${-Lagrangian} surfaces in almost {Hermitian} manyfolds},
     journal = {Sbornik. Mathematics},
     pages = {379--391},
     year = {1990},
     volume = {67},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1990_67_2_a3/}
}
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Lê Hông Vân. The minimal $\Phi$-Lagrangian surfaces in almost Hermitian manyfolds. Sbornik. Mathematics, Tome 67 (1990) no. 2, pp. 379-391. http://geodesic.mathdoc.fr/item/SM_1990_67_2_a3/

[1] Dao Chong Tkhi, Fomenko A. T., Minimalnye poverkhnosti i problema Plato, Nauka, M., 1987 | MR | Zbl

[2] Dao Chong Tkhi, “O minimalnykh veschestvennykh potokakh na kompaktnykh rimanovykh mnogoobraziyakh”, Izv. AN SSSR. Ser. matem., 41 (1977), 853–867 | Zbl

[3] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, Nauka, M., 1981

[4] Le Khong Van, Fomenko A. T., “Lagranzhevy mnogoobraziya i indeks Maslova v teorii minimalnykh poverkhnostei”, DAN SSSR, 299 (1988), 42–45 | Zbl

[5] Le Khong Van, “Minimalnye poverkhnosti i formy kalibrovki v simmetricheskikh prostranstvakh”, Tr. seminara po vekt. i tenz. analizu, 22, Izd-vo MGU, M., 1985, 107–118

[6] Likhnerovich A., Teoriya svyaznostei v tselom i gruppy golonomii, IL, M., 1960

[7] Federer G., Geometricheskaya teoriya mery, Nauka, M., 1987 | MR | Zbl

[8] Bryant R., Minimal Lagrangian submanifold of Kahler–Einstein, Manifolds. Preprint IHES, 1985 | MR

[9] Harvey R., Lawson B., “Calibrated Geometries”, Acta Math., 148 (1982), 47–157 | DOI | MR | Zbl

[10] Herman R., “The second variation for minimal submanifolds”, J. Math. Mech., 16 (1966), 473–491 | MR | Zbl

[11] Simons J., “Minimal varieties in Riemannian manifolds”, Ann. Math., 88 (1968), 62–105 ; имеется перевод: Математика (сб. переводов), 16:6 (1972), 60–104 | DOI | MR | Zbl | Zbl